Tourism Development of Traditional Villages:A case study of Shanxijie Village,Dawenkou Town,Tai'an City

Traditional villages are an important carrier of Chinese civilization, carrying the historical memory of the Chinese nation. Tourism development has become an effective way to protect traditional villages and a special way to modernize traditional villages. In this paper, the conditions for tourism development in Shanxijie Village, Dawenkou Town, Tai’an City were analyzed, and the existing problems in its tourism development were discussed. Meanwhile, corresponding strategies for tourism development were put forward to guide Shanxijie Village to embark on a high-quality tourism development road.

Approximately orthogonal nonnegative Tucker decomposition for flexible multiway clustering

High-order tensor data are prevalent in real-world applications, and multiway clustering is one of the most important techniques for exploratory data mining and compression of multiway data. However, existing multiway clustering is based on the K-means procedure and is incapable of addressing the issue of crossed membership degrees. To overcome this limitation, we propose a flexible multiway clustering model called approximately orthogonal nonnegative Tucker decomposition(AONTD). The new model provides extra flexibility to handle crossed memberships while fully exploiting the multilinear property of tensor data.The accelerated proximal gradient method and the low-rank compression tricks are adopted to optimize the cost function. The experimental results on both synthetic data and real-world cases illustrate that the proposed AONTD model outperforms the benchmark clustering methods by significantly improving the interpretability and robustness.

Semi-supervised non-negative Tucker decomposition for tensor data representation

Non-negative Tucker decomposition(NTD) has been developed as a crucial method for non-negative tensor data representation.However, NTD is essentially an unsupervised method and cannot take advantage of label information. In this paper, we claim that the low-dimensional representation extracted by NTD can be treated as the predicted soft-clustering coefficient matrix and can therefore be learned jointly with label propagation in a unified framework. The proposed method can extract the physicallymeaningful and parts-based representation of tensor data in their natural form while fully exploring the potential ability of the given labels with a nearest neighbors graph. In addition, an efficient accelerated proximal gradient(APG) algorithm is developed to solve the optimization problem. Finally, the experimental results on five benchmark image data sets for semi-supervised clustering and classification tasks demonstrate the superiority of this method over state-of-the-art methods.

Semi-supervised multi-view clustering with dual hypergraph regularized partially shared non-negative matrix factorization

Real-world data can often be represented in multiple forms and views,and analyzing data from different perspectives allows for more comprehensive learning of the data,resulting in better data clustering results.Non-negative matrix factorization(NMF)is used to solve the clustering problem to extract uniform discriminative low-dimensional features from multi-view data.Many clustering methods based on graph regularization have been proposed and proven to be effective,but ordinary graphs only consider pairwise relationships between samples.In order to learn the higher-order relationships that exist in the sample manifold and feature manifold of multi-view data,we propose a new semi-supervised multi-view clustering method called dual hypergraph regularized partially shared non-negative matrix factorization(DHPS-NMF).The complex manifold structure of samples and features is learned by constructing samples and feature hypergraphs.To improve the discrimination power of the obtained lowdimensional features,semi-supervised regression terms are incorporated into the model to effectively use the label information when capturing the complex manifold structure of the data.Ultimately,we conduct experiments on six real data sets and the results show that our algorithm achieves encouraging results in comparison with some methods.

Robust tensor decomposition via orientation invariant tubal nuclear norms

Aiming at recovering an unknown tensor(i.e.,multi-way array)corrupted by both sparse outliers and dense noises,robust tensor decomposition(RTD)serves as a powerful pre-processing tool for subsequent tasks like classification and target detection in many computer vision and machine learning applications.Recently,tubal nuclear norm(TNN)based optimization is proposed with superior performance as compared with other tensorial nuclear norms for tensor recovery.However,one major limitation is its orientation sensitivity due to low-rankness strictly defined along tubal orientation and it cannot simultaneously model spectral low-rankness in multiple orientations.To this end,we introduce two new tensor norms called OITNN-O and OITNN-L to exploit multi-orientational spectral low-rankness for an arbitrary K-way(K≥3)tensors.We further formulate two RTD models via the proposed norms and develop two algorithms as the solutions.Theoretically,we establish non-asymptotic error bounds which can predict the scaling behavior of the estimation error.Experiments on real-world datasets demonstrate the superiority and effectiveness of the proposed norms.

Preface

Tensor decomposition and tensor networks(TNs)are factorizations of high order tensors into a network of low-order tensors,which have been studied in quantum physics,chemistry and applied mathematics.In recent years,TNs have been increasingly investigated and applied to machine learning and AI fields,due to its significant efficacy in modeling large-scale and high-order data,representing model parameters in deep neural networks,and accelerating computations for learning algorithms.In particular,TNs have been exploited to solve several challenging problems in data completion,model compression,multimodal fusion,multitask knowledge sharing and theoretical analysis of deep neural networks.More potential technologies using TNs are rapidly emerging and finding many interesting applications in machine learning,such as modeling probability functions,probabilistic graphical models and implementing efficient TN computations in GPU.However,the topic of TNs in machine learning is relatively young and many open problems are still not fully explored.This special topic aims to promote research and development related to innovative TNs technology from perspectives of fundamental theory and algorithms,novel approaches in machine learning and deep neural networks,and various applications in computer vision,biomedical image processing and many other related fields.